Is it Possible 4 input XOR gate ? if not then why ?
Can you please provide the "definition" you are referring to?You cannot make a XOR gate with three or more inputs (by the definition).
Exactly, but that would not be a XOR gate. If you cascade two or more XOR gates, that's what you get.I could be wrong about this, but a multi-input xor gate would provide a high output when an odd number of inputs are high. Basically, an odd parity generator.
XOR is associative, but the resulting "gate" wouldn't be a XOR. A true 3 input XOR gate would have its output high only if one and only one of its inputs is high.Sure you can make a 3 input gate because XOR is an associative operation. It is also commutative, but that it not necessarily relevant here. It is called Boolean Algebra for a reason. It satisfies the necessary and sufficient conditions to be called that. The definition is quite precise. for the same reason that three is possible, four or more is also possible. In addition it can be expressed in terms of the operations of inversion, AND, and OR.
Why is the output high when all inputs are high? Does that mean it's more like an odd/parity indicator? Where is the OR? I would have expected a HIGH at the ouput when only 1 input is HIGH...http://www.nxp.com/documents/data_sheet/74LVC1G386.pdf
I can hardly wait to hear the weasel words on this one.
Don't forget that a XOR is a complex operation, based on ANDs, ORs and NOTs. Associativity doesn't play well with XORs, especially if other operations are involved. I was not careful enough and made mistakes because I did overlook this same aspect, when doing some boolean algebra.This argument is wrong. The logical AND is also a 2 bit operation, as is OR, Peirce Arrow, and Sheffer Stroke. Listen carefully and pay attention. ANY associative binary operation can be cascaded in such a way as to produce the same output as a multi input gate. To argue otherwise is just plain wrong. I'm sorry to put such a sharp edge on my comments but mathematics is what it is and not what you think it should be.
Would you be more convinced by an actual datasheet?
http://www.nxp.com/documents/data_sheet/74LVC1G386.pdf
I can hardly wait to hear the weasel words on this one.
I ask the same question too. I predicted that cascading two XOR gates would lead to something like this. But why is that called an exclusive OR? Wouldn't that be some kind of misnomer?Why is the output high when all inputs are high? Does that mean it's more like an odd/parity indicator? Where is the OR? I would have expected a HIGH at the ouput when only 1 input is HIGH...
I'm sure the reason why the OP asked that question is because there is no definition someone put in words for a 4-input XOR gate. The only definition you will find is one for a 2-input XOR gate. I assume for simplification purposes they write that both inputs have to be different or only one input can be HIGH for the output to go HIGH. This is where confusion starts because if you assume the same to be valid for more than 2 inputs then the above diagram and the XOR gate PapaBravo posted wouldn't be XOR gates.If we are to accept that the following two configurations represent a 3-input XOR function, then the two circuits give identical results and we can say the XOR operator is associative.
The result is an odd-parity generator circuit and also for a 4-input circuit.